Estimation of Systematic and Spatially Correlated Components of Random Signals from Repeated Measurements: Application to Contrast Enhanced Computer Tomography Measurements

Abstract

Observational errors can be categorized into two groups: random noise, which is altered every time when measurement is repeated, and a systematic temporally invariant error. In this paper, we propose a method to estimate the covariance structure for systematic error and random noise using a small number of repeated measurements of the signal. We model the systematic and random components as stationary Gaussian random fields and use the Bayesian approach to estimate the spatial covariance functions of these components simultaneously. The study is motivated by an application related to the diagnosis of joint diseases using contrast enhanced computer tomography (CT) measurements. The noise in the measured contrast agent concentration profiles within cartilage tissue is strongly spatially correlated and includes a systematic component. Since the estimates are significantly sensitive to all errors in modeling, the systematic error and random noise components should be characterized for reliable estimation. The method proposed in this paper can be used to construct approximative covariance matrices for the observational noise using a small number of CT measurements. The capabilities of the proposed method are demonstrated using numerical simulations and also real CT data corresponding to measurements of contrast agent diffusion profile in cartilage.